Alice, Bob and Charlie play a game.
Alice writes down two positive integers on a blackboard visible to Bob and Charlie. She says that one of them is of her own choice, the other number is the sum of two positive integers, which were secretly communicated before by Bob and Charlie, respectively. Now Alice asks Bob, if he knows Charlies number. If he says "NO", the corresponding question goes to Charlie. If he says "NO", the question goes to Bob and so forth.

Can we expect a "Yes" answer at some point?